A norm refinement of Bezout's Lemma, and quaternion orders

Abstract: Given coprime integers a,b, the classical identity of Bezout provides integers u,v such that au-bv = 1. We consider refinements to this identity, where we ask that u,v are norms from a quadratic extension. We then find ourselves counting optimal embeddings of a quadratic order in a quaternion order, for which we give explicit formulas in many cases. This is joint work with Donald Cartwright and Xavier Roulleau.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar